A=1x2x3x4+2x3x4x5+3x4x5x6+...+97x98x99x100

5xA=1x2x3x4+2x3x4x5x(6-1)+3x4x5x6x(7-2)+...+97x98x99x100x(101-96)

5xA=1x2x3x4x5+2x3x4x5x6-1x2x3x4x5+3x4x5x6x7-2x3x4x5x6+...+97x98x99x100x101-96x97x98x99x100

5xA=97x98x99x100x101

A=97x98x99x101x20=1901009880

=1901009880

A=1x2x3x4+2x3x4x5+3x4x5x6+...+97x98x99x100

5xA=1x2x3x4+2x3x4x5x(6-1)+3x4x5x6x(7-2)+...+97x98x99x100x(101-96)

5xA=1x2x3x4x5+2x3x4x5x6-1x2x3x4x5+3x4x5x6x7-2x3x4x5x6+...+97x98x99x100x101-96x97x98x99x100

5xA=97x98x99x100x101

A=97x98x99x101x20=1901009880

\(3xC=\frac{3}{1x2x3x4}+\frac{3}{2x3x4x5}+...+\frac{3}{97x98x99x100}\)

\(3xC=\frac{4-1}{1x2x3x4}+\frac{5-2}{2x3x4x5}+...+\frac{100-97}{97x98x99x100}\)

\(3xC=\frac{1}{1x2x3}-\frac{1}{2x3x4}+\frac{1}{2x3x4}+\frac{1}{3x4x5}+...+\frac{1}{97x98x99}-\frac{1}{98x99x100}\)

\(3xC=\frac{1}{1x2x3}-\frac{1}{98x99x100}\Rightarrow C=\frac{\frac{1}{6}-\frac{1}{98x99x100}}{3}\)

Chào người đẹp

nhân hai vế với 3.ta được 
3S = 3/(1.2.3.4) + 3/(2.3.4.5) + ....+3/(2011.2012.2013.2014) 
<=> 3S = 1/(1.2.3) - 1/(2.3.4) + 1/(2.3.4) - 1/(3.4.5) +....+1/(2011.2012.2013) - 1/(2012.2013.2014) 
<=> 3 S = 1/6-1/(2012.2013.2014) 
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